Stochastic modeling of non-equilibrium quantum systems

Abstract

In this project we propose a study of open quantum systems described by the Lindblad formalism, using different theoretical and computational tools. The project is divided into four parts. The first concerns an effective description of magnon-magnon collisions in magnonic crystals. The goal is to obtain an analytically tractable equation to describe the attenuation of the magnonic flux due to magnon-magnon interactions. The second part concerns the numerical implementation of the Density Matrix Renormalization Group to obtain the non- equilibrium steady-state of open quantum spin chains subject to two reservoirs kept at different temperatures. Thirdly, we propose to study the effect of dephasing noises in the heat flux of fermionic and bosonic chains. And, lastly, we propose to study the rectification of the heat and magnetization fluxes in one- dimensional spin chains, relating the results with the Onsager reciprocal relations. It is hoped that these analyzes will contribute to improve our understanding of the properties of non-equilibrium quantum systems, an area of great current importance in the context of condensed matter physics. (AU)